双调和函数梯度范数的一个估计
An Estimation of the Gradient Norm of Biharmonic Functions
DOI: 10.12677/PM.2023.1310296, PDF,   
作者: 贾宝蕊：天津职业技术师范大学理学院，天津
关键词: 双解析函数；双调和函数；Poisson核；梯度范数；Bianalytic Functions； Biharmonic Function； Poisson Kernel； Gradient Norm
摘要: 双调和函数在数学界具有重要地位，且在现实中有广泛的应用。本文主要探究的是双调和函数梯度范数的一个估计，通过分析双调和函数与双解析函数的关系，计算出双调和函数的Poisson核，由此给出有界双调和函数梯度范数的一个估计，得到的积分表达式为今后进一步探究双调和函数的Khavinson猜想打下基础。
Abstract: Biharmonic functions play an important role in the field of mathematics and have wide applications in reality. This article mainly explores an estimate of the gradient norm of biharmonic functions. By analyzing the relationship between biharmonic functions and bianalytic functions, the Poisson kernel of biharmonic functions is calculated, and an estimate of the gradient norm of bounded biharmonic functions is given. The obtained integral expression lays the foundation for further exploration of the Khavinson conjecture of biharmonic functions in the future.
文章引用：贾宝蕊. 双调和函数梯度范数的一个估计[J]. 理论数学, 2023, 13(10): 2900-2907. https://doi.org/10.12677/PM.2023.1310296

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